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Search: id:A155725
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| A155725 |
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Symmetrical product form polynomial as triangle sequence coefficients: q(x,n)=Product[x + 2*n - i + 1, {i, 0, n - 1}]; p(x,n)=q(x,n)+x^2+x^n*q(1/x,m);t(n,m)=coefficients(p(x,n). |
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+0
1
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| 2, 4, 4, 21, 18, 21, 211, 125, 125, 211, 3025, 1680, 670, 1680, 3025, 55441, 31639, 7960, 7960, 31639, 55441, 1235521, 725655, 178199, 45570, 178199, 725655, 1235521, 32432401, 19471584, 4988326, 765289, 765289, 4988326, 19471584
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Row sums are:
{2, 8, 60, 672, 10080, 190080, 4324320, 115315200, 3528645120, 121898649600,
4693098009600,...}.
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FORMULA
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q(x,n)=Product[x + 2*n - i + 1, {i, 0, n - 1}];
p(x,n)=q(x,n)+x^2+x^n*q(1/x,m);
t(n,m)=coefficients(p(x,n).
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EXAMPLE
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{2},
{4, 4},
{21, 18, 21},
{211, 125, 125, 211},
{3025, 1680, 670, 1680, 3025},
{55441, 31639, 7960, 7960, 31639, 55441},
{1235521, 725655, 178199, 45570, 178199, 725655, 1235521},
{32432401, 19471584, 4988326, 765289, 765289, 4988326, 19471584, 32432401},
{980179201, 598482108, 159173510, 24219972, 4535538, 24219972, 159173510, 598482108, 980179201}, {33522128641, 20742534711, 5681716170, 904550030, 98395248, 98395248, 904550030, 5681716170, 20742534711, 33522128641},
{1279935820801, 800575997925, 224518871346, 37179349350, 4041096653, 595737450, 4041096653, 37179349350, 224518871346, 800575997925, 1279935820801}
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MATHEMATICA
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Clear[p, a, b, c, d, n, q, q2, x];
q[x_, n_] = Product[x + 2*n - i + 1, {i, 0, n - 1}];
p[x_, n_] = q[x, n] + x^n*q[1/x, n];
Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A088042 A013140 A155720 this_sequence A103973 A129826 A009296
Adjacent sequences: A155722 A155723 A155724 this_sequence A155726 A155727 A155728
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 25 2009
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